# Re: [tlaplus] Proving inductive predicates in TLAPS

 Hello,TLAPS unfortunately doesn't handle quantification over tuples [1]. You have to rewrite your definitions as follows for the proof of the lemma to work:Extend(A) == A \cup { bc \in Blocks \X Blocks: <> \in A }A0 == { bc \in Blocks \X Blocks: bc[1]=bc[2] }I didn't look at the rest of the module, please feel free to come back if you run into more trouble.StephanOn 12 Nov 2020, at 09:05, 'Leander Jehl' via tlaplus wrote:I have a specification with constant Blocks and a function prev \in [Blocks -> Blocks] that defines a tree.I would like to define an ancestor relation on that tree and prove statements like reflexivity and transitivity.If I try to prove NatInductiveDefConclusion, it triggers a bug in TLAPS.I would be grateful for any tips on how to define the ancestor relation, or how to avoid the bug.Here is my current definition of the ancestor relation:Extend(A) == A \cup { <> \in Blocks \X Blocks: <> \in A }A0 == { <> \in Blocks \X Blocks: b=c }ancestors[i \in Nat] == IF i=0 THEN A0                                        ELSE Extend(ancestors[i-1])Ancestor(b,c) == /\ height[b] <= height[c]                                /\ height[c] - height[b] \in Nat                                /\ <> \in ancestors[height[c] - height[b]]My complete tree specification can be found here: https://github.com/leandernikolaus/hotstuff-ivy/blob/master/Tree.tlaThanks,Leander -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/8bbc83f3-9900-4230-baa5-c3f5af7d0514n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/F453ACCD-9685-475D-AA89-C867E4B4EEF5%40gmail.com.